{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from scipy.stats import poisson\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "MAX_CARS = 20\n",
    "MOVING_COST_OF_CAR = 2\n",
    "RENTAL_GET_OF_CAR = 10\n",
    "RENTAL_REQUEST_OF_FIRST_LOCATION = 3\n",
    "RENTAL_REQUEST_OF_SECOND_LOCATION = 4\n",
    "RETURN_NUM_OF_FIRST_LOCATION = 3\n",
    "RETURN_NUM_OF_SECOND_LOCATION = 2\n",
    "DISCOUNT = 0.9\n",
    "\n",
    "FREE_NUM_OF_CARS = 10\n",
    "COST_STOP_OF_CAR = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "poisson_cache = dict()\n",
    "POISSON_UPPER_BOUND = 10\n",
    "def poisson_prob(k, lam):\n",
    "    global poisson_cache\n",
    "    key = k * 10 + lam\n",
    "    if key not in poisson_cache:\n",
    "        poisson_cache[key] = poisson.pmf(k, lam)\n",
    "    return poisson_cache[key]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_return(state, action, state_value, constanted_return_car=True):\n",
    "    returns = 0.0\n",
    "    returns -= abs(action) * MOVING_COST_OF_CAR\n",
    "    # current car\n",
    "    NUM_OF_CAR_FIRST_LOC = min(state[0] - action, MAX_CARS)\n",
    "    NUM_OF_CAR_SECOND_LOC = min(state[1] + action, MAX_CARS)\n",
    "    \n",
    "    for rental_num_of_car_first_loc in range(POISSON_UPPER_BOUND):\n",
    "        for rental_num_of_car_second_loc in range(POISSON_UPPER_BOUND):\n",
    "            prob = poisson_prob(rental_num_of_car_first_loc, RENTAL_REQUEST_OF_FIRST_LOCATION) * \\\n",
    "                poisson_prob(rental_num_of_car_second_loc, RENTAL_REQUEST_OF_SECOND_LOCATION)\n",
    "            num_of_car_first_loc = NUM_OF_CAR_FIRST_LOC\n",
    "            num_of_car_second_loc = NUM_OF_CAR_SECOND_LOC\n",
    "            valid_rental_first_loc = min(NUM_OF_CAR_FIRST_LOC, rental_num_of_car_first_loc)\n",
    "            valid_rental_second_loc = min(NUM_OF_CAR_SECOND_LOC, rental_num_of_car_second_loc)\n",
    "            rewards = (valid_rental_first_loc + valid_rental_second_loc) * RENTAL_GET_OF_CAR\n",
    "            num_of_car_first_loc -= valid_rental_first_loc\n",
    "            num_of_car_second_loc -= valid_rental_second_loc\n",
    "            \n",
    "            if constanted_return_car:\n",
    "                return_car_first_loc = RETURN_NUM_OF_FIRST_LOCATION\n",
    "                return_car_second_loc = RETURN_NUM_OF_SECOND_LOCATION\n",
    "                num_of_car_first_loc = min(num_of_car_first_loc + return_car_first_loc, MAX_CARS)\n",
    "                num_of_car_second_loc = min(num_of_car_second_loc + return_car_second_loc, MAX_CARS)\n",
    "                returns += prob * (rewards + DISCOUNT * state_value[num_of_car_first_loc, num_of_car_second_loc])\n",
    "            else:\n",
    "                for return_car_first_loc in range(POISSON_UPPER_BOUND):\n",
    "                    for return_car_second_loc in range(POISSON_UPPER_BOUND):\n",
    "                        prob_return = poisson_prob(return_car_first_loc, RETURN_NUM_OF_FIRST_LOCATION) * \\\n",
    "                                poisson_prob(return_car_second_loc, RETURN_NUM_OF_SECOND_LOCATION)\n",
    "                        num_of_car_first_loc_ = min(num_of_car_first_loc + return_car_first_loc, MAX_CARS)\n",
    "                        num_of_car_second_loc_ = min(num_of_car_second_loc + return_car_second_loc, MAX_CARS)\n",
    "                        returns += prob * prob_return * (rewards + DISCOUNT * state_value[num_of_car_first_loc_, num_of_car_second_loc_])\n",
    "\n",
    "    return returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "policy stable True\n"
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      "text/plain": [
       "<Figure size 4000x2000 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# maximum # of cars to move during night\n",
    "MAX_MOVE_OF_CARS = 5\n",
    "# all possible actions\n",
    "actions = np.arange(-MAX_MOVE_OF_CARS, MAX_MOVE_OF_CARS + 1)\n",
    "\n",
    "def figure_4_2(constant_returned_cars=True):\n",
    "    value = np.zeros((MAX_CARS + 1, MAX_CARS + 1))\n",
    "    policy = np.zeros(value.shape, dtype=np.int32)\n",
    "\n",
    "    iterations = 0\n",
    "    _, axes = plt.subplots(2, 3, figsize=(40, 20))\n",
    "    plt.subplots_adjust(wspace=0.1, hspace=0.2)\n",
    "    axes = axes.flatten()\n",
    "    while True:\n",
    "        fig = sns.heatmap(np.flipud(policy), cmap=\"YlGnBu\", ax=axes[iterations])\n",
    "        fig.set_ylabel('# cars at first location', fontsize=30)\n",
    "        fig.set_yticks(list(reversed(range(MAX_CARS + 1))))\n",
    "        fig.set_xlabel('# cars at second location', fontsize=30)\n",
    "        fig.set_title('policy {}'.format(iterations), fontsize=30)\n",
    "\n",
    "        # # policy evaluation (in-place)\n",
    "        # while True:\n",
    "        #     old_value = value.copy()\n",
    "        #     for i in range(MAX_CARS + 1):\n",
    "        #         for j in range(MAX_CARS + 1):\n",
    "        #             new_state_value = expected_return([i, j], policy[i, j], value, constanted_return_car=constant_returned_cars)\n",
    "        #             value[i, j] = new_state_value\n",
    "        #     max_value_change = abs(old_value - value).max()\n",
    "        #     print('max value change {}'.format(max_value_change))\n",
    "        #     if max_value_change < 1e-4:\n",
    "        #         break\n",
    "        # policy improvement\n",
    "        while True:\n",
    "            old_value = value.copy()\n",
    "            policy_stable = True\n",
    "            for i in range(MAX_CARS + 1):\n",
    "                for j in range(MAX_CARS + 1):\n",
    "                    old_action = policy[i, j]\n",
    "                    actions_returns = []\n",
    "                    for action in actions:\n",
    "                        if -j <= action <= i:\n",
    "                            actions_returns.append(expected_return([i, j], action, value, constanted_return_car=constant_returned_cars))\n",
    "                        else:\n",
    "                            actions_returns.append(-np.inf)\n",
    "                    new_action = actions[np.argmax(actions_returns)]\n",
    "                    policy[i, j] = new_action\n",
    "                    new_state_value = max(actions_returns)\n",
    "                    value[i, j] = new_state_value\n",
    "                    if policy_stable and old_action != new_action:\n",
    "                        policy_stable = False\n",
    "            max_value_change = abs(old_value - value).max()\n",
    "            print('max value change {}'.format(max_value_change))\n",
    "            if max_value_change < 1e-4:\n",
    "                break\n",
    " \n",
    "        print('policy stable {}'.format(policy_stable))\n",
    "        if policy_stable:\n",
    "            fig = sns.heatmap(np.flipud(value), cmap=\"YlGnBu\", ax=axes[-1])\n",
    "            fig.set_ylabel('# cars at first location', fontsize=30)\n",
    "            fig.set_yticks(list(reversed(range(MAX_CARS + 1))))\n",
    "            fig.set_xlabel('# cars at second location', fontsize=30)\n",
    "            fig.set_title('optimal value', fontsize=30)\n",
    "            break\n",
    "\n",
    "        iterations += 1\n",
    "figure_4_2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "rl",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.20"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
